## Implicit Hybrid Block Collocation Method for the Solution of Volterra Integral Equation of the Second Kind

Published: 2023-07-05

Page: 218-228

D. Raymond

Department of Mathematics and Statistics, Federal University Wukari, Nigeria.

Department of Mathematics and Statistics, Federal University Wukari, Nigeria.

R. Ajia

Department of Mathematics and Statistics, College of Agriculture, Science and Technology, Jalingo, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

This paper proposes a three-step hybrid block method with two off-grid collocation points that solves Volterra integral equation of the second kind. The collocation of power series and trigonometric approach was used as the basis function to generate the continuous hybrid linear multistep method, which was then evaluated at non-interpolating points to give a continuous block method. The discrete block method was recovered when the continuous block was evaluated at all step points. The basic properties of the methods were investigated and were found to be zero-stable, consistent and convergent. The effectiveness of the developed three-step method is applied to solve some Volterra integral equations of the second kind by converting into an initial value problems of ordinary differential equations and from the numerical results obtained, it is observed that our methods gives better approximation than the existing method compared with.

Keywords: Trigonometric, hybrid point, second kind, Volterra integral, power series

#### How to Cite

Raymond , D., Adu , A., & Ajia , R. (2023). Implicit Hybrid Block Collocation Method for the Solution of Volterra Integral Equation of the Second Kind. Asian Journal of Pure and Applied Mathematics, 5(1), 218–228. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1826

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